IGCSE Maths: Kinematics Key Points | IGCSE 数学：运动学考点精讲

📚 IGCSE Maths: Kinematics Key Points | IGCSE 数学：运动学考点精讲

Kinematics is the branch of mathematics that describes the motion of objects without considering the forces that cause the motion. In IGCSE Maths, you will learn how to use graphs, equations, and vector concepts to model movement along a straight line. This article breaks down all the essential topics you need to master, from distance-time graphs to SUVAT equations, with clear explanations and practical exam tips.

运动学是数学的一个分支，描述物体的运动而不考虑引起运动的力。在 IGCSE 数学中，你将学习如何使用图表、方程和矢量概念来模拟沿直线的运动。本文分解了你需要掌握的所有基本主题，从距离-时间图到匀加速运动方程，并附有清晰的解释和实用的考试技巧。

1. Introduction to Kinematics | 运动学导论

Kinematics deals with quantities like displacement, velocity, and acceleration. In IGCSE, we mainly study motion in one dimension (along a straight line). Problems often involve a moving car, a falling object, or a runner. You need to be able to describe motion in words, using numbers, and through graphs.

运动学研究位移、速度和加速度等物理量。在 IGCSE 中，我们主要研究一维运动（沿直线）。题目通常涉及行驶的汽车、下落的物体或跑步者。你需要能够用文字、数字和图表来描述运动。

It is important to distinguish between everyday language and precise scientific terms. For example, “speed” and “velocity” are not the same in kinematics. Understanding these definitions perfectly is the first step to solving exam questions correctly.

区分日常用语和精确的科学术语非常重要。例如，“速率”和“速度”在运动学中并不相同。准确理解这些定义是正确解答考试题目的第一步。

2. Scalars and Vectors | 标量与矢量

Scalars are quantities that have only magnitude (size). Examples include distance, speed, and time. Vectors have both magnitude and direction, such as displacement, velocity, and acceleration. In IGCSE, direction is often indicated by a positive or negative sign along a straight line.

标量是只有大小（量值）的量。例子包括距离、速率和时间。矢量既有大小又有方向，例如位移、速度和加速度。在 IGCSE 中，方向通常用沿直线的正号或负号表示。

When a car travels 20 m to the right and then 5 m to the left, the total distance is 25 m (scalar), but the displacement is 15 m to the right (vector). Always check whether the question asks for a scalar or a vector, as missing the direction can lose marks.

当一辆汽车向右行驶 20 m 然后向左行驶 5 m，总距离是 25 m（标量），但位移是向右 15 m（矢量）。一定要检查题目要求的是标量还是矢量，因为遗漏方向会丢分。

3. Displacement, Velocity and Acceleration | 位移、速度和加速度

Displacement (s) is the straight-line distance in a given direction from start to finish. Velocity (v) is the rate of change of displacement: v = s / t if constant. Acceleration (a) is the rate of change of velocity: a = (v − u) / t, where u is initial velocity and v is final velocity.

位移（s）是从起点到终点在给定方向上的直线距离。速度（v）是位移的变化率：如果恒定，则 v = s / t。加速度（a）是速度的变化率：a = (v − u) / t，其中 u 是初速度，v 是末速度。

Units of displacement are metres (m), velocity m/s, acceleration m/s². If acceleration is negative while velocity is positive, the object is slowing down (deceleration). In IGCSE, you often need to convert km/h to m/s: divide by 3.6.

位移的单位是米 (m)，速度是 m/s，加速度是 m/s²。如果加速度为负而速度为正，则物体正在减速。在 IGCSE 中，你经常需要将 km/h 转换为 m/s：除以 3.6。

4. Distance-Time Graphs | 距离-时间图

A distance-time graph shows how distance changes over time. Time is plotted on the horizontal axis (x-axis) and distance on the vertical axis (y-axis). The gradient of the graph represents speed. A steeper line means faster motion, while a horizontal line indicates the object is stationary.

距离-时间图显示距离如何随时间变化。时间位于横轴（x 轴），距离位于纵轴（y 轴）。图的梯度表示速率。更陡的线意味着运动更快，而水平线表示物体静止。

If a distance-time graph is a straight line sloping upwards, speed is constant. A curved line means the speed is changing—acceleration or deceleration. To find speed at an instant from a curve, draw a tangent and calculate its gradient.

如果距离-时间图是一条向上倾斜的直线，则速率恒定。曲线表示速率在变化——加速或减速。要从曲线上求瞬时速率，可画切线并计算其梯度。

Be careful: the gradient of a distance-time graph gives speed, not velocity, because distance does not indicate direction. Exam questions may ask you to calculate average speed from total distance divided by total time.

注意：距离-时间图的梯度给出的是速率，而不是速度，因为距离不指示方向。考试题可能要求你通过总距离除以总时间来计算平均速率。

5. Speed-Time Graphs | 速度-时间图

A speed-time graph plots speed on the y-axis and time on the x-axis. The gradient of the line shows acceleration. A positive gradient means increasing speed (acceleration), a negative gradient means decreasing speed (deceleration), and zero gradient means constant speed.

速度-时间图在 y 轴标出速率，x 轴标出时间。线的梯度表示加速度。正梯度意味着速率增加（加速），负梯度意味着速率减小（减速），零梯度表示匀速运动。

The area under a speed-time graph represents the distance travelled. This is a crucial concept often tested in IGCSE. You may need to find area by counting squares or using formulas for rectangles and triangles.

速度-时间图下的面积表示行走的距离。这是一个重要的概念，经常在 IGCSE 中考查。你可能需要通过数格或用矩形和三角形面积公式来求面积。

If the graph shows velocity instead of speed (direction matters), then area below x-axis represents displacement in the opposite direction. IGCSE usually uses speed-time graphs, but always read the axis label carefully.

如果图显示的是速度而非速率（方向有关），则 x 轴下方的面积表示相反方向的位移。IGCSE 通常使用速度-时间图，但务必仔细阅读轴标签。

6. Area under Speed-Time Graph | 速度-时间图下方面积

Calculating the area under a speed-time graph gives the total distance moved. For a constant speed graph, distance = speed × time, which is the area of a rectangle. For uniform acceleration, the shape is a trapezium, and area = ½ (u + v) t.

计算速度-时间图下的面积可得出移动的总距离。对于恒定速率图，距离 = 速率 × 时间，即矩形面积。对于匀加速运动，形状为梯形，面积 = ½ (u + v) t。

If the graph is made of different sections (e.g. accelerating, constant speed, braking), split the area into rectangles, triangles, and trapeziums. Sum the areas to find total distance. This method avoids memorising too many formulas and works for any shape.

如果图由不同部分组成（例如加速、匀速、刹车），可将面积分割成矩形、三角形和梯形。将面积求和以求出总距离。这种方法避免了记忆太多公式，适用于任何形状。

Always check the units on axes: if speed is in km/h and time in hours, distance will be in km. If speed in m/s and time in seconds, distance is in m. Convert units if necessary before calculations.

始终检查轴上的单位：如果速率以 km/h 为单位，时间以小时为单位，则距离单位为 km。如果速率以 m/s 为单位，时间以秒为单位，则距离单位为 m。如有必要，在计算前转换单位。

7. Uniformly Accelerated Motion (SUVAT) | 匀加速运动 (SUVAT)

When acceleration is constant, we use the four SUVAT equations. They link five quantities: s (displacement), u (initial velocity), v (final velocity), a (acceleration), and t (time). You must know three to find the other two.

当加速度恒定时，我们使用四个 SUVAT 方程。它们联系五个物理量：s（位移）、u（初速度）、v（末速度）、a（加速度）和 t（时间）。你必须知道其中三个才能求出另外两个。

The equations are:

v = u + at

s = ½ (u + v) t

s = ut + ½ at²

v² = u² + 2as

Choose the equation that does not contain the unknown quantity you do not need. For example, if you need to find s but do not know v, use s = ut + ½ at².

选择不包含你不需要的未知量的方程。例如，如果你需要求 s 但不知道 v，请使用 s = ut + ½ at²。

These equations are powerful. They only work when acceleration is constant. In IGCSE, many problems involve a car accelerating uniformly, a ball falling freely, or a rocket launching. Always define a positive direction and assign signs accordingly.

这些方程非常有用。它们仅在加速度恒定时有效。在 IGCSE 中，许多问题涉及汽车匀加速、球自由下落或火箭发射。始终定义正方向并相应地赋予符号。

8. Free Fall and Acceleration due to Gravity | 自由落体与重力加速度

An object falling freely near the Earth’s surface experiences constant acceleration due to gravity, denoted by g. Its approximate value is 9.8 m/s², but in IGCSE maths problems, it is often taken as 10 m/s² to simplify calculations. The direction is downwards.

物体在地球表面附近自由下落时会受到恒定的重力加速度，记作 g。其近似值为 9.8 m/s²，但在 IGCSE 数学题中通常取 10 m/s² 以简化计算。方向向下。

If you throw a ball vertically upwards, the acceleration throughout its flight is g downwards (negative if up is positive). At the highest point, velocity is zero momentarily, but acceleration is still g downwards. Use SUVAT equations with a = −g (if upward positive) to model the motion.

如果你向上竖直抛球，在整个飞行过程中加速度始终为向下的 g（若向上为正，则为负）。在最高点，速度瞬间为零，但加速度仍为向下的 g。使用 SUVAT 方程，令 a = −g（若向上为正）来模拟运动。

Common exam questions ask for the time to reach maximum height, the maximum height itself, or the total time of flight. Remember that for a ball returning to its starting height, the final velocity is equal in magnitude but opposite in direction to the initial velocity.

常见的考试题要求计算到达最大高度的时间、最大高度本身或总飞行时间。记住，对于返回起始高度的球，末速度的大小等于初速度但方向相反。

9. Interpreting Kinematic Graphs | 解读运动学图表

You will often be given a graph and asked to describe the motion in stages. For a speed-time graph, look at the gradient and the area. For a distance-time graph, look at the gradient. Practice reading values from graphs, calculating acceleration, and finding distance from area.

你通常会得到一个图表并要求分段描述运动。对于速度-时间图，观察梯度和面积。对于距离-时间图，观察梯度。练习从图表中读取数值，计算加速度，并根据面积求距离。

Be prepared to sketch graphs from a verbal description of motion. For example, “A car accelerates from rest to 20 m/s in 5 s, travels at constant speed for 10 s, then decelerates uniformly to rest in 4 s.” Translate this into a speed-time graph with labelled axes.

准备好根据对运动的文字描述来绘制草图。例如，“一辆汽车从静止加速到 20 m/s 用时 5 秒，匀速行驶 10 秒，然后匀减速至静止用时 4 秒”。将其转换成带有标签的轴的速度-时间图。

Sometimes you need to convert between distance-time and speed-time graphs. The gradient of the distance-time plot gives the corresponding speed-time value. Reverse construction is more difficult and beyond IGCSE scope, but understanding the link is essential.

有时你需要在距离-时间图和速度-时间图之间转换。距离-时间图的梯度给出相应的速度-时间值。逆向作图更难且超出 IGCSE 范围，但理解其联系至关重要。

10. Problem-Solving Strategies | 解题策略

When solving kinematics problems, first list the known quantities: s, u, v, a, t. Identify which three you know and which you need to find. Then select the appropriate SUVAT equation. Draw a simple diagram with arrows indicating direction.

在解运动学题目时，首先列出已知量：s、u、v、a、t。确定你知道哪三个以及你需要求哪一个。然后选择合适的 SUVAT 方程。画一个简单的示意图，用箭头标明方向。

For graph questions, start by examining the axes labels and units. Note the shape: straight lines mean constant gradient (constant velocity or acceleration), curves indicate changing gradient. Break the motion into sections if the graph has different parts.

对于图表题，首先检查轴标签和单位。注意形状：直线意味着恒定梯度（恒定速度或加速度），曲线表示变化的梯度。如果图表有不同的部分，将运动分段。

Always check whether your final answer makes sense. For example, if you calculate a distance that is negative when it should be positive, you might have mixed up directions. Double-check signs and units.

始终检查你的最终答案是否合理。例如，如果你计算出的距离是负的而本应为正，你可能混淆了方向。仔细检查符号和单位。

11. Common Mistakes to Avoid | 常见错误

Confusing distance and displacement, speed and velocity. Distance and speed are scalars; displacement and velocity are vectors. Read the question to know which one is required.

混淆距离和位移、速率和速度。距离和速率是标量；位移和速度是矢量。阅读题目以确定需要哪一个。
Using the wrong SUVAT equation. Make sure you know which variable is missing and pick the equation that excludes it.

使用了错误的 SUVAT 方程。确保你知道缺少哪个变量，并选择不含它的方程。
Forgetting to square units when using v² = u² + 2as. Velocity squared may be large; always take the square root correctly.

在使用 v² = u² + 2as 时忘记单位平方。速度的平方可能很大；始终正确开方。
Ignoring the sign of acceleration due to gravity. In free fall, a = −g if upward is positive. Many candidates lose marks because they get a negative time or distance incorrectly.

忽略了重力加速度的符号。在自由落体中，如果向上为正，a = −g。许多考生因为错误地得到负的时间或距离而丢分。
Mixing units: e.g. using km/h with seconds. Always convert to m/s before using SUVAT, unless all units are consistent.

单位混用：例如将 km/h 与秒一起使用。在使用 SUVAT 之前始终转换为 m/s，除非所有单位一致。

12. Exam Tips for Kinematics | 运动学考试技巧

In an exam, show all your working clearly. Write down the SUVAT equation you are using, substitute the numbers with units, and then state the answer with correct units. Even if your final answer is wrong, you can get method marks.

在考试中，清晰地展示所有步骤。写下你使用的 SUVAT 方程，代入带单位的数字，然后陈述带正确单位的答案。即使最终答案错了，你也能得到方法分。

For graph sketching, use a ruler for straight lines and label the axes. Indicate key values like final speed or time intervals. If the question asks for an estimate from a curve, draw the tangent carefully and show how you calculate the gradient.

对于绘制的图表，用尺子画直线并标记坐标轴。标明关键值如末速度或时间间隔。如果题目要求根据曲线估算，仔细画切线并展示你如何计算梯度。

Practice past paper questions under timed conditions. Kinematics graphs and SUVAT problems are very common, and with practice you can learn to recognise the typical patterns quickly. Always check the mark scheme to understand how marks are allocated.

在限时条件下练习历年真题。运动学图表和 SUVAT 问题非常常见，通过练习你可以学会快速识别典型模式。务必查看评分方案，了解分数是如何分配的。

Published by TutorHao | IGCSE Maths Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）

IGCSE Maths: Kinematics Key Points | IGCSE 数学：运动学 考点精讲